Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
3701 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 3701 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C9⋊#997 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D9⋊#997 | C2 | 1 | 2 | yes | maximal, direct product factor |
| 3 | C2×D3×#997 | — | 3 | 1 | no | maximal |
| 4 | C2×D9×H(5,𝔽2) | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C22×D9⋊A4 | — | 4 | 3 | no | maximal |
| 6 | C9⋊#997 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×D9⋊SL(2,𝔽3) | — | 4 | 2 | no | maximal |
| 8 | C2×C3×#997 | D3 | 1 | 1 | yes | characteristic |
| 9 | D3×#997 | — | 3 | 2 | no | — |
| 10 | C2×C9×H(5,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | D9×H(5,𝔽2) | — | 3 | 4 | no | — |
| 12 | D9×H(5,𝔽2) | — | 3 | 6 | no | — |
| 13 | D9×H(5,𝔽2) | C2×C3 | 1 | 2 | yes | complemented |
| 14 | C2×#63715 | — | 3 | 2 | no | — |
| 15 | C2×#41×D9 | — | 3 | 2 | no | — |
| 16 | C2×#63710 | — | 3 | 3 | no | — |
| 17 | C22×D4×D9 | — | 3 | 3 | no | — |
| 18 | C2×#63703 | — | 2 | 1 | no | — |
| 19 | C22×C9⋊A4 | — | 4 | 3 | no | — |
| 20 | C2×D9⋊A4 | — | 4 | 12 | no | — |
| 21 | C2×D9⋊A4 | — | 4 | 6 | no | — |
| 22 | C2×C9⋊SL(2,𝔽3) | — | 4 | 2 | no | — |
| 23 | D9⋊SL(2,𝔽3) | — | 4 | 4 | no | — |
| 24 | C2×D3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 25 | C22×#997 | — | 9 | 1 | no | — |
| 26 | C22×D3×A4 | — | 12 | 3 | no | — |
| 27 | C3×#997 | C2×D3 | 1 | 1 | yes | characteristic |
| 28 | C2×D3×SL(2,𝔽3) | — | 12 | 2 | no | — |
| 29 | C24×D9 | — | 3 | 1 | no | — |
| 30 | C24×D9 | A4 | 1 | 3 | yes | complemented |
| 31 | C9×H(5,𝔽2) | — | 3 | 2 | no | — |
| 32 | C9×H(5,𝔽2) | — | 3 | 3 | no | — |
| 33 | C9×H(5,𝔽2) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×C9×#41 | — | 3 | 2 | no | — |
| 35 | C22×D4×C9 | — | 3 | 3 | no | — |
| 36 | C22×#611 | — | 3 | 3 | no | — |
| 37 | C22×#611 | — | 3 | 3 | no | — |
| 38 | #63715 | — | 3 | 12 | no | — |
| 39 | #63715 | — | 3 | 12 | no | — |
| 40 | #63715 | — | 3 | 4 | no | — |
| 41 | #63715 | — | 3 | 4 | no | — |
| 42 | #41×D9 | — | 3 | 12 | no | — |
| 43 | #41×D9 | — | 3 | 12 | no | — |
| 44 | #41×D9 | — | 3 | 4 | no | — |
| 45 | #41×D9 | — | 3 | 4 | no | — |
| 46 | C2×#3701 | — | 3 | 2 | no | — |
| 47 | C2×Q8×D9 | A4 | 1 | 2 | yes | complemented |
| 48 | #63710 | — | 3 | 6 | no | — |
| 49 | #63710 | — | 3 | 24 | no | — |
| 50 | #63710 | — | 3 | 6 | no | — |
| 51 | #63710 | — | 3 | 6 | no | — |
| 52 | #63710 | — | 3 | 6 | no | — |
| 53 | C2×#3699 | — | 3 | 6 | no | — |
| 54 | C2×D4×D9 | — | 3 | 6 | no | — |
| 55 | C2×D4×D9 | — | 3 | 12 | no | — |
| 56 | C2×D4×D9 | — | 3 | 6 | no | — |
| 57 | C2×D4×D9 | — | 3 | 24 | no | — |
| 58 | C2×D4×D9 | — | 3 | 6 | no | — |
| 59 | C2×D4×D9 | — | 3 | 6 | no | — |
| 60 | C2×D4×D9 | — | 3 | 6 | no | — |
| 61 | C2×#3697 | — | 3 | 6 | no | — |
| 62 | C22×D36 | — | 3 | 3 | no | — |
| 63 | C22×C4×D9 | — | 3 | 3 | no | — |
| 64 | #63703 | — | 2 | 1 | no | — |
| 65 | C22×AGL(1,ℤ/9) | — | 16 | 1 | no | — |
| 66 | C2×C9⋊A4 | — | 4 | 6 | no | — |
| 67 | C2×C9⋊A4 | — | 4 | 3 | no | — |
| 68 | D9⋊A4 | — | 4 | 12 | no | — |
| 69 | C9⋊SL(2,𝔽3) | — | 4 | 2 | no | — |
| 70 | C2×C3×H(5,𝔽2) | C3×D3 | 1 | 1 | yes | characteristic |
| 71 | D3×H(5,𝔽2) | — | 3 | 2 | no | — |
| 72 | D3×H(5,𝔽2) | — | 9 | 4 | no | — |
| 73 | D3×H(5,𝔽2) | — | 9 | 6 | no | — |
| 74 | C2×#1009 | — | 9 | 2 | no | — |
| 75 | C2×D3×#41 | — | 9 | 2 | no | — |
| 76 | C2×#1004 | — | 9 | 3 | no | — |
| 77 | C22×D3×D4 | — | 9 | 3 | no | — |
| 78 | C2×#997 | — | 3 | 1 | no | — |
| 79 | C2×#997 | — | 9 | 2 | no | — |
| 80 | C22×C3×A4 | — | 4 | 3 | no | — |
| 81 | C2×D3×A4 | — | 12 | 6 | no | — |
| 82 | C2×D3×A4 | — | 12 | 12 | no | — |
| 83 | C2×C3×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 84 | D3×SL(2,𝔽3) | — | 12 | 4 | no | — |
| 85 | C24×C9 | — | 3 | 1 | no | — |
| 86 | C24×C9 | C2×A4 | 1 | 3 | yes | complemented |
| 87 | C23×D9 | — | 3 | 3 | no | — |
| 88 | C23×D9 | — | 3 | 6 | no | — |
| 89 | C23×D9 | — | 3 | 2 | no | — |
| 90 | C23×D9 | — | 3 | 3 | no | — |
| 91 | C23×D9 | — | 3 | 3 | no | — |
| 92 | C23×D9 | — | 3 | 6 | no | — |
| 93 | C23×D9 | — | 4 | 12 | no | — |
| 94 | C23×D9 | — | 12 | 4 | no | — |
| 95 | C23×D9 | C2×A4 | 1 | 6 | yes | complemented |
| 96 | C22×C22⋊C9 | — | 8 | 3 | no | — |
| 97 | C9×#41 | — | 3 | 6 | no | — |
| 98 | C9×#41 | — | 3 | 6 | no | — |
| 99 | C9×#41 | — | 3 | 2 | no | — |
| 100 | C9×#41 | — | 3 | 2 | no | — |
| 101 | C2×Q8×C9 | C2×A4 | 1 | 2 | yes | complemented |
| 102 | C2×D4×C9 | — | 3 | 6 | no | — |
| 103 | C2×D4×C9 | — | 3 | 3 | no | — |
| 104 | C2×D4×C9 | — | 3 | 12 | no | — |
| 105 | C2×D4×C9 | — | 3 | 3 | no | — |
| 106 | C2×D4×C9 | — | 3 | 3 | no | — |
| 107 | C2×D4×C9 | — | 3 | 3 | no | — |
| 108 | C22×C4×C9 | — | 3 | 3 | no | — |
| 109 | C2×#611 | — | 3 | 12 | no | — |
| 110 | C2×#611 | — | 3 | 12 | no | — |
| 111 | C2×#611 | — | 3 | 12 | no | — |
| 112 | C2×#611 | — | 3 | 6 | no | — |
| 113 | C2×#611 | — | 3 | 6 | no | — |
| 114 | C2×#611 | — | 3 | 6 | no | — |
| 115 | C2×#611 | — | 3 | 6 | no | — |
| 116 | C22×Dic9 | — | 3 | 3 | no | — |
| 117 | #3701 | — | 3 | 12 | no | — |
| 118 | #3701 | — | 3 | 4 | no | — |
| 119 | Q8×D9 | — | 3 | 4 | no | — |
| 120 | Q8×D9 | C2×A4 | 1 | 4 | yes | complemented |
| 121 | #3699 | — | 3 | 24 | no | — |
| 122 | #3699 | — | 3 | 12 | no | — |
| 123 | #3699 | — | 3 | 12 | no | — |
| 124 | D4×D9 | — | 3 | 24 | no | — |
| 125 | D4×D9 | — | 3 | 12 | no | — |
| 126 | D4×D9 | — | 3 | 12 | no | — |
| 127 | D4×D9 | — | 3 | 24 | no | — |
| 128 | D4×D9 | — | 3 | 24 | no | — |
| 129 | D4×D9 | — | 3 | 24 | no | — |
| 130 | D4×D9 | — | 3 | 24 | no | — |
| 131 | #3697 | — | 3 | 12 | no | — |
| 132 | #3697 | — | 3 | 12 | no | — |
| 133 | #3697 | — | 3 | 12 | no | — |
| 134 | #3697 | — | 3 | 12 | no | — |
| 135 | C2×D36 | — | 3 | 6 | no | — |
| 136 | C2×D36 | — | 3 | 12 | no | — |
| 137 | C2×D36 | — | 3 | 6 | no | — |
| 138 | C2×D36 | — | 3 | 6 | no | — |
| 139 | C2×C4×D9 | — | 3 | 6 | no | — |
| 140 | C2×C4×D9 | — | 3 | 6 | no | — |
| 141 | C2×C4×D9 | — | 3 | 12 | no | — |
| 142 | C2×C4×D9 | — | 3 | 6 | no | — |
| 143 | C2×C4×D9 | — | 3 | 2 | no | — |
| 144 | C2×Dic18 | — | 3 | 2 | no | — |
| 145 | C2×Q8⋊C9 | — | 8 | 2 | no | — |
| 146 | C22×H(5,𝔽2) | — | 9 | 1 | no | Sylow |
| 147 | C22×3−1+2 | — | 16 | 1 | no | — |
| 148 | C2×AGL(1,ℤ/9) | — | 16 | 4 | no | — |
| 149 | C2×AGL(1,ℤ/9) | — | 16 | 2 | no | — |
| 150 | C9⋊A4 | — | 4 | 3 | no | — |
| 151 | C24×D3 | — | 3 | 3 | no | — |
| 152 | C24×D3 | — | 9 | 1 | no | — |
| 153 | C23×A4 | — | 36 | 3 | no | — |
| 154 | C3×H(5,𝔽2) | — | 3 | 2 | no | — |
| 155 | C3×H(5,𝔽2) | — | 3 | 3 | no | — |
| 156 | C3×H(5,𝔽2) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 157 | C2×C3×#41 | — | 3 | 2 | no | — |
| 158 | C22×C3×D4 | — | 3 | 3 | no | — |
| 159 | C22×#67 | — | 9 | 3 | no | — |
| 160 | C22×#67 | — | 9 | 3 | no | — |
| 161 | #1009 | — | 9 | 12 | no | — |
| 162 | #1009 | — | 9 | 12 | no | — |
| 163 | #1009 | — | 9 | 4 | no | — |
| 164 | #1009 | — | 9 | 4 | no | — |
| 165 | D3×#41 | — | 9 | 4 | no | — |
| 166 | D3×#41 | — | 9 | 4 | no | — |
| 167 | D3×#41 | — | 9 | 12 | no | — |
| 168 | D3×#41 | — | 9 | 12 | no | — |
| 169 | C2×#239 | — | 9 | 2 | no | — |
| 170 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 171 | #1004 | — | 9 | 6 | no | — |
| 172 | #1004 | — | 9 | 24 | no | — |
| 173 | #1004 | — | 9 | 6 | no | — |
| 174 | #1004 | — | 9 | 6 | no | — |
| 175 | #1004 | — | 9 | 6 | no | — |
| 176 | C2×#237 | — | 9 | 6 | no | — |
| 177 | C2×D3×D4 | — | 9 | 6 | no | — |
| 178 | C2×D3×D4 | — | 9 | 6 | no | — |
| 179 | C2×D3×D4 | — | 9 | 6 | no | — |
| 180 | C2×D3×D4 | — | 9 | 12 | no | — |
| 181 | C2×D3×D4 | — | 9 | 6 | no | — |
| 182 | C2×D3×D4 | — | 9 | 24 | no | — |
| 183 | C2×D3×D4 | — | 9 | 6 | no | — |
| 184 | C2×#235 | — | 9 | 6 | no | — |
| 185 | C22×D12 | — | 9 | 3 | no | — |
| 186 | C22×C4×D3 | — | 9 | 3 | no | — |
| 187 | #997 | — | 3 | 1 | no | — |
| 188 | C22×SL(2,𝔽3) | — | 36 | 2 | no | — |
| 189 | C22×C3×D3 | — | 48 | 1 | no | — |
| 190 | C2×C3×A4 | — | 4 | 6 | no | — |
| 191 | C2×C3×A4 | — | 4 | 3 | no | — |
| 192 | D3×A4 | — | 12 | 12 | no | — |
| 193 | C3×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 194 | C23×C9 | — | 3 | 3 | no | — |
| 195 | C23×C9 | — | 3 | 1 | no | — |
| 196 | C23×C9 | — | 3 | 3 | no | — |
| 197 | C23×C9 | — | 3 | 3 | no | — |
| 198 | C23×C9 | — | 4 | 6 | no | — |
| 199 | C23×C9 | — | 12 | 2 | no | — |
| 200 | C23×C9 | C22×A4 | 1 | 3 | yes | complemented |
| 201 | C22×D9 | — | 3 | 3 | no | — |
| 202 | C22×D9 | — | 3 | 6 | no | — |
| 203 | C22×D9 | — | 3 | 6 | no | — |
| 204 | C22×D9 | — | 3 | 6 | no | — |
| 205 | C22×D9 | — | 3 | 6 | no | — |
| 206 | C22×D9 | — | 3 | 6 | no | — |
| 207 | C22×D9 | — | 3 | 6 | no | — |
| 208 | C22×D9 | — | 4 | 12 | no | — |
| 209 | C22×D9 | — | 6 | 12 | no | — |
| 210 | C22×D9 | — | 12 | 4 | no | — |
| 211 | C22×D9 | — | 12 | 12 | no | — |
| 212 | C22×D9 | — | 12 | 6 | no | — |
| 213 | C22×D9 | — | 12 | 12 | no | — |
| 214 | C22×D9 | — | 12 | 6 | no | — |
| 215 | C22×D9 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 216 | C2×C22⋊C9 | — | 8 | 6 | no | — |
| 217 | C2×C22⋊C9 | — | 8 | 3 | no | — |
| 218 | Q8×C9 | — | 3 | 2 | no | — |
| 219 | Q8×C9 | C22×A4 | 1 | 2 | yes | complemented |
| 220 | D4×C9 | — | 3 | 12 | no | — |
| 221 | D4×C9 | — | 3 | 6 | no | — |
| 222 | D4×C9 | — | 3 | 6 | no | — |
| 223 | C2×C4×C9 | — | 3 | 3 | no | — |
| 224 | C2×C4×C9 | — | 3 | 6 | no | — |
| 225 | C2×C4×C9 | — | 3 | 3 | no | — |
| 226 | C2×C4×C9 | — | 3 | 2 | no | — |
| 227 | #611 | — | 3 | 24 | no | — |
| 228 | #611 | — | 3 | 24 | no | — |
| 229 | C2×Dic9 | — | 3 | 6 | no | — |
| 230 | C2×Dic9 | — | 3 | 6 | no | — |
| 231 | C2×Dic9 | — | 3 | 2 | no | — |
| 232 | D36 | — | 3 | 12 | no | — |
| 233 | D36 | — | 3 | 12 | no | — |
| 234 | C4×D9 | — | 3 | 12 | no | — |
| 235 | C4×D9 | — | 3 | 12 | no | — |
| 236 | C4×D9 | — | 3 | 4 | no | — |
| 237 | C4×D9 | — | 3 | 4 | no | — |
| 238 | Dic18 | — | 3 | 4 | no | — |
| 239 | Dic18 | — | 3 | 4 | no | — |
| 240 | Q8⋊C9 | — | 8 | 2 | no | — |
| 241 | C2×H(5,𝔽2) | — | 9 | 2 | no | — |
| 242 | C2×H(5,𝔽2) | — | 27 | 3 | no | — |
| 243 | C2×H(5,𝔽2) | — | 27 | 2 | no | — |
| 244 | C2×H(5,𝔽2) | — | 27 | 4 | no | — |
| 245 | C2×H(5,𝔽2) | — | 27 | 6 | no | — |
| 246 | C2×H(5,𝔽2) | AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 247 | C22×#41 | — | 27 | 2 | no | — |
| 248 | C23×D4 | — | 27 | 3 | no | — |
| 249 | C2×3−1+2 | — | 16 | 2 | no | — |
| 250 | C2×3−1+2 | — | 16 | 1 | no | — |
| 251 | AGL(1,ℤ/9) | — | 16 | 4 | no | — |
| 252 | C24×C3 | — | 3 | 1 | no | — |
| 253 | C24×C3 | D3×A4 | 1 | 3 | yes | — |
| 254 | C23×D3 | — | 3 | 6 | no | — |
| 255 | C23×D3 | — | 9 | 3 | no | — |
| 256 | C23×D3 | — | 9 | 3 | no | — |
| 257 | C23×D3 | — | 9 | 2 | no | — |
| 258 | C23×D3 | — | 9 | 6 | no | — |
| 259 | C23×D3 | — | 9 | 3 | no | — |
| 260 | C23×D3 | — | 9 | 6 | no | — |
| 261 | C23×D3 | — | 12 | 12 | no | — |
| 262 | C23×D3 | — | 36 | 4 | no | — |
| 263 | C22×A4 | — | 12 | 3 | no | — |
| 264 | C22×A4 | — | 36 | 6 | no | — |
| 265 | C22×A4 | — | 36 | 12 | no | — |
| 266 | C3×#41 | — | 3 | 6 | no | — |
| 267 | C3×#41 | — | 3 | 6 | no | — |
| 268 | C3×#41 | — | 3 | 2 | no | — |
| 269 | C3×#41 | — | 3 | 2 | no | — |
| 270 | C2×C3×Q8 | D3×A4 | 1 | 2 | yes | — |
| 271 | C2×C3×D4 | — | 3 | 6 | no | — |
| 272 | C2×C3×D4 | — | 3 | 3 | no | — |
| 273 | C2×C3×D4 | — | 3 | 12 | no | — |
| 274 | C2×C3×D4 | — | 3 | 3 | no | — |
| 275 | C2×C3×D4 | — | 3 | 3 | no | — |
| 276 | C2×C3×D4 | — | 3 | 3 | no | — |
| 277 | C22×C3×C4 | — | 3 | 3 | no | — |
| 278 | C2×#67 | — | 9 | 12 | no | — |
| 279 | C2×#67 | — | 9 | 12 | no | — |
| 280 | C2×#67 | — | 9 | 6 | no | — |
| 281 | C2×#67 | — | 9 | 12 | no | — |
| 282 | C2×#67 | — | 9 | 6 | no | — |
| 283 | C2×#67 | — | 9 | 6 | no | — |
| 284 | C2×#67 | — | 9 | 6 | no | — |
| 285 | C22×Dic3 | — | 9 | 3 | no | — |
| 286 | #239 | — | 9 | 12 | no | — |
| 287 | #239 | — | 9 | 4 | no | — |
| 288 | D3×Q8 | — | 3 | 4 | no | — |
| 289 | D3×Q8 | — | 9 | 4 | no | — |
| 290 | #237 | — | 9 | 24 | no | — |
| 291 | #237 | — | 9 | 12 | no | — |
| 292 | #237 | — | 9 | 12 | no | — |
| 293 | D3×D4 | — | 9 | 12 | no | — |
| 294 | D3×D4 | — | 9 | 12 | no | — |
| 295 | D3×D4 | — | 9 | 24 | no | — |
| 296 | D3×D4 | — | 9 | 24 | no | — |
| 297 | D3×D4 | — | 9 | 24 | no | — |
| 298 | D3×D4 | — | 9 | 24 | no | — |
| 299 | D3×D4 | — | 9 | 24 | no | — |
| 300 | #235 | — | 9 | 12 | no | — |
| 301 | #235 | — | 9 | 12 | no | — |
| 302 | #235 | — | 9 | 12 | no | — |
| 303 | #235 | — | 9 | 12 | no | — |
| 304 | C2×D12 | — | 9 | 6 | no | — |
| 305 | C2×D12 | — | 9 | 12 | no | — |
| 306 | C2×D12 | — | 9 | 6 | no | — |
| 307 | C2×D12 | — | 9 | 6 | no | — |
| 308 | C2×C4×D3 | — | 9 | 2 | no | — |
| 309 | C2×C4×D3 | — | 9 | 6 | no | — |
| 310 | C2×C4×D3 | — | 9 | 6 | no | — |
| 311 | C2×C4×D3 | — | 9 | 12 | no | — |
| 312 | C2×C4×D3 | — | 9 | 6 | no | — |
| 313 | C2×Dic6 | — | 9 | 2 | no | — |
| 314 | C2×SL(2,𝔽3) | — | 12 | 2 | no | — |
| 315 | C2×SL(2,𝔽3) | — | 36 | 4 | no | — |
| 316 | C22×C32 | — | 16 | 1 | no | — |
| 317 | C2×C3×D3 | — | 48 | 4 | no | — |
| 318 | C2×C3×D3 | — | 48 | 2 | no | — |
| 319 | C3×A4 | — | 4 | 3 | no | — |
| 320 | C22×C9 | — | 3 | 3 | no | — |
| 321 | C22×C9 | — | 3 | 3 | no | — |
| 322 | C22×C9 | — | 4 | 3 | no | — |
| 323 | C22×C9 | — | 6 | 6 | no | — |
| 324 | C22×C9 | — | 12 | 3 | no | — |
| 325 | C22×C9 | — | 12 | 1 | no | — |
| 326 | C22×C9 | — | 12 | 3 | no | — |
| 327 | C22×C9 | — | 32 | 1 | no | — |
| 328 | C22×C9 | C2×C22⋊A4 | 1 | 1 | yes | characteristic |
| 329 | C2×D9 | — | 3 | 6 | no | — |
| 330 | C2×D9 | — | 6 | 6 | no | — |
| 331 | C2×D9 | — | 6 | 12 | no | — |
| 332 | C2×D9 | — | 6 | 12 | no | — |
| 333 | C2×D9 | — | 12 | 6 | no | — |
| 334 | C2×D9 | — | 12 | 6 | no | — |
| 335 | C2×D9 | — | 12 | 6 | no | — |
| 336 | C2×D9 | — | 12 | 6 | no | — |
| 337 | C2×D9 | #997 | 1 | 4 | yes | complemented |
| 338 | C2×D9 | C2×C22⋊A4 | 1 | 2 | yes | — |
| 339 | C22⋊C9 | — | 8 | 3 | no | — |
| 340 | C4×C9 | — | 3 | 2 | no | — |
| 341 | C4×C9 | — | 3 | 2 | no | — |
| 342 | Dic9 | — | 3 | 4 | no | — |
| 343 | C25 | — | 9 | 3 | no | — |
| 344 | C25 | — | 27 | 1 | no | — |
| 345 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 346 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 347 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 348 | H(5,𝔽2) | — | 27 | 24 | no | — |
| 349 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 350 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 351 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 352 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 353 | H(5,𝔽2) | — | 27 | 12 | no | — |
| 354 | H(5,𝔽2) | — | 27 | 12 | no | — |
| 355 | H(5,𝔽2) | — | 27 | 4 | no | — |
| 356 | H(5,𝔽2) | C2×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 357 | C2×#41 | — | 3 | 2 | no | — |
| 358 | C2×#41 | — | 27 | 6 | no | — |
| 359 | C2×#41 | — | 27 | 6 | no | — |
| 360 | C2×#41 | — | 27 | 4 | no | — |
| 361 | C2×#41 | — | 27 | 4 | no | — |
| 362 | C2×#41 | — | 27 | 12 | no | — |
| 363 | C2×#41 | — | 27 | 12 | no | — |
| 364 | C2×#41 | — | 27 | 2 | no | — |
| 365 | C22×Q8 | — | 9 | 2 | no | — |
| 366 | C22×D4 | — | 3 | 3 | no | — |
| 367 | C22×D4 | — | 27 | 3 | no | — |
| 368 | C22×D4 | — | 27 | 6 | no | — |
| 369 | C22×D4 | — | 27 | 6 | no | — |
| 370 | C22×D4 | — | 27 | 6 | no | — |
| 371 | C22×D4 | — | 27 | 12 | no | — |
| 372 | C22×D4 | — | 27 | 6 | no | — |
| 373 | C22×D4 | — | 27 | 24 | no | — |
| 374 | C22×D4 | — | 27 | 6 | no | — |
| 375 | C22×D4 | — | 27 | 3 | no | — |
| 376 | C22×D4 | — | 27 | 3 | no | — |
| 377 | C23×C4 | — | 27 | 3 | no | — |
| 378 | 3−1+2 | — | 16 | 1 | no | Sylow |
| 379 | C23×C3 | — | 3 | 1 | no | — |
| 380 | C23×C3 | — | 3 | 3 | no | — |
| 381 | C23×C3 | — | 3 | 3 | no | — |
| 382 | C23×C3 | — | 3 | 3 | no | — |
| 383 | C23×C3 | — | 4 | 6 | no | — |
| 384 | C23×C3 | — | 12 | 2 | no | — |
| 385 | C23×C3 | — | 144 | 1 | no | — |
| 386 | C23×C3 | C2×D3×A4 | 1 | 3 | yes | — |
| 387 | C22×D3 | — | 3 | 1 | no | — |
| 388 | C22×D3 | — | 9 | 6 | no | — |
| 389 | C22×D3 | — | 9 | 6 | no | — |
| 390 | C22×D3 | — | 9 | 3 | no | — |
| 391 | C22×D3 | — | 9 | 6 | no | — |
| 392 | C22×D3 | — | 9 | 6 | no | — |
| 393 | C22×D3 | — | 9 | 6 | no | — |
| 394 | C22×D3 | — | 9 | 6 | no | — |
| 395 | C22×D3 | — | 12 | 12 | no | — |
| 396 | C22×D3 | — | 18 | 12 | no | — |
| 397 | C22×D3 | — | 36 | 4 | no | — |
| 398 | C22×D3 | — | 36 | 12 | no | — |
| 399 | C22×D3 | — | 36 | 6 | no | — |
| 400 | C22×D3 | — | 36 | 12 | no | — |
| 401 | C22×D3 | — | 36 | 6 | no | — |
| 402 | C2×A4 | — | 12 | 6 | no | — |
| 403 | C2×A4 | — | 12 | 3 | no | — |
| 404 | C2×A4 | — | 36 | 12 | no | — |
| 405 | C3×Q8 | — | 3 | 2 | no | — |
| 406 | C3×Q8 | C2×D3×A4 | 1 | 2 | yes | — |
| 407 | C3×D4 | — | 3 | 6 | no | — |
| 408 | C3×D4 | — | 3 | 6 | no | — |
| 409 | C3×D4 | — | 3 | 12 | no | — |
| 410 | C2×C3×C4 | — | 3 | 3 | no | — |
| 411 | C2×C3×C4 | — | 3 | 6 | no | — |
| 412 | C2×C3×C4 | — | 3 | 3 | no | — |
| 413 | C2×C3×C4 | — | 3 | 2 | no | — |
| 414 | #67 | — | 9 | 24 | no | — |
| 415 | #67 | — | 9 | 24 | no | — |
| 416 | C2×Dic3 | — | 9 | 6 | no | — |
| 417 | C2×Dic3 | — | 9 | 6 | no | — |
| 418 | C2×Dic3 | — | 9 | 2 | no | — |
| 419 | D12 | — | 9 | 12 | no | — |
| 420 | D12 | — | 9 | 12 | no | — |
| 421 | C4×D3 | — | 9 | 4 | no | — |
| 422 | C4×D3 | — | 9 | 4 | no | — |
| 423 | C4×D3 | — | 9 | 12 | no | — |
| 424 | C4×D3 | — | 9 | 12 | no | — |
| 425 | Dic6 | — | 9 | 4 | no | — |
| 426 | Dic6 | — | 9 | 4 | no | — |
| 427 | SL(2,𝔽3) | — | 12 | 2 | no | — |
| 428 | C2×C32 | — | 16 | 2 | no | — |
| 429 | C2×C32 | — | 16 | 1 | no | — |
| 430 | C3×D3 | — | 48 | 4 | no | — |
| 431 | C2×C9 | — | 6 | 3 | no | — |
| 432 | C2×C9 | — | 6 | 3 | no | — |
| 433 | C2×C9 | — | 32 | 2 | no | — |
| 434 | C2×C9 | — | 32 | 1 | no | — |
| 435 | C2×C9 | C2×#997 | 1 | 2 | yes | complemented |
| 436 | C2×C9 | C22×C22⋊A4 | 1 | 1 | yes | characteristic |
| 437 | D9 | — | 6 | 6 | no | — |
| 438 | D9 | C2×#997 | 1 | 4 | yes | complemented |
| 439 | C24 | — | 3 | 1 | no | — |
| 440 | C24 | — | 9 | 6 | no | — |
| 441 | C24 | — | 27 | 3 | no | — |
| 442 | C24 | — | 27 | 2 | no | — |
| 443 | C24 | — | 27 | 6 | no | — |
| 444 | C24 | — | 27 | 3 | no | — |
| 445 | C24 | — | 27 | 3 | no | — |
| 446 | C24 | — | 27 | 6 | no | — |
| 447 | C24 | — | 36 | 12 | no | — |
| 448 | C24 | — | 108 | 4 | no | — |
| 449 | C24 | D9⋊A4 | 1 | 3 | yes | complemented |
| 450 | #41 | — | 3 | 6 | no | — |
| 451 | #41 | — | 3 | 6 | no | — |
| 452 | #41 | — | 3 | 2 | no | — |
| 453 | #41 | — | 3 | 2 | no | — |
| 454 | #41 | — | 27 | 12 | no | — |
| 455 | #41 | — | 27 | 12 | no | — |
| 456 | #41 | — | 27 | 12 | no | — |
| 457 | #41 | — | 27 | 12 | no | — |
| 458 | #41 | — | 27 | 12 | no | — |
| 459 | #41 | — | 27 | 12 | no | — |
| 460 | #41 | — | 27 | 24 | no | — |
| 461 | #41 | — | 27 | 12 | no | — |
| 462 | #41 | — | 27 | 4 | no | — |
| 463 | C2×Q8 | — | 9 | 4 | no | — |
| 464 | C2×Q8 | — | 27 | 2 | no | — |
| 465 | C2×Q8 | — | 27 | 4 | no | — |
| 466 | C2×Q8 | D9⋊A4 | 1 | 2 | yes | complemented |
| 467 | C2×D4 | — | 3 | 6 | no | — |
| 468 | C2×D4 | — | 3 | 3 | no | — |
| 469 | C2×D4 | — | 3 | 12 | no | — |
| 470 | C2×D4 | — | 3 | 3 | no | — |
| 471 | C2×D4 | — | 3 | 3 | no | — |
| 472 | C2×D4 | — | 3 | 3 | no | — |
| 473 | C2×D4 | — | 27 | 6 | no | — |
| 474 | C2×D4 | — | 27 | 12 | no | — |
| 475 | C2×D4 | — | 27 | 6 | no | — |
| 476 | C2×D4 | — | 27 | 6 | no | — |
| 477 | C2×D4 | — | 27 | 12 | no | — |
| 478 | C2×D4 | — | 27 | 12 | no | — |
| 479 | C2×D4 | — | 27 | 24 | no | — |
| 480 | C2×D4 | — | 27 | 24 | no | — |
| 481 | C2×D4 | — | 27 | 24 | no | — |
| 482 | C2×D4 | — | 27 | 24 | no | — |
| 483 | C2×D4 | — | 27 | 24 | no | — |
| 484 | C2×D4 | — | 27 | 12 | no | — |
| 485 | C2×D4 | — | 27 | 12 | no | — |
| 486 | C2×D4 | — | 27 | 6 | no | — |
| 487 | C2×D4 | — | 27 | 6 | no | — |
| 488 | C2×D4 | — | 27 | 6 | no | — |
| 489 | C2×D4 | — | 27 | 12 | no | — |
| 490 | C2×D4 | — | 27 | 6 | no | — |
| 491 | C22×C4 | — | 3 | 3 | no | — |
| 492 | C22×C4 | — | 27 | 2 | no | — |
| 493 | C22×C4 | — | 27 | 6 | no | — |
| 494 | C22×C4 | — | 27 | 12 | no | — |
| 495 | C22×C4 | — | 27 | 6 | no | — |
| 496 | C22×C4 | — | 27 | 6 | no | — |
| 497 | C22×C4 | — | 27 | 3 | no | — |
| 498 | C22×C3 | — | 3 | 3 | no | — |
| 499 | C22×C3 | — | 3 | 3 | no | — |
| 500 | C22×C3 | — | 4 | 3 | no | — |
| 501 | C22×C3 | — | 6 | 6 | no | — |
| 502 | C22×C3 | — | 12 | 3 | no | — |
| 503 | C22×C3 | — | 12 | 1 | no | — |
| 504 | C22×C3 | — | 12 | 3 | no | — |
| 505 | C22×C3 | — | 48 | 1 | no | — |
| 506 | C22×C3 | — | 144 | 2 | no | — |
| 507 | C22×C3 | — | 144 | 4 | no | — |
| 508 | C22×C3 | D3×C22⋊A4 | 1 | 1 | yes | characteristic |
| 509 | C2×D3 | — | 3 | 4 | no | — |
| 510 | C2×D3 | — | 3 | 2 | no | — |
| 511 | C2×D3 | — | 9 | 6 | no | — |
| 512 | C2×D3 | — | 18 | 12 | no | — |
| 513 | C2×D3 | — | 18 | 12 | no | — |
| 514 | C2×D3 | — | 18 | 6 | no | — |
| 515 | C2×D3 | — | 36 | 6 | no | — |
| 516 | C2×D3 | — | 36 | 6 | no | — |
| 517 | C2×D3 | — | 36 | 6 | no | — |
| 518 | C2×D3 | — | 36 | 6 | no | — |
| 519 | A4 | — | 12 | 3 | no | — |
| 520 | C3×C4 | — | 3 | 2 | no | — |
| 521 | C3×C4 | — | 3 | 2 | no | — |
| 522 | Dic3 | — | 9 | 4 | no | — |
| 523 | C32 | — | 16 | 1 | no | — |
| 524 | C9 | — | 32 | 1 | no | — |
| 525 | C9 | C22×#997 | 1 | 1 | yes | characteristic, complemented |
| 526 | C23 | — | 3 | 1 | no | — |
| 527 | C23 | — | 3 | 3 | no | — |
| 528 | C23 | — | 3 | 3 | no | — |
| 529 | C23 | — | 3 | 3 | no | — |
| 530 | C23 | — | 4 | 6 | no | — |
| 531 | C23 | — | 9 | 1 | no | — |
| 532 | C23 | — | 12 | 2 | no | — |
| 533 | C23 | — | 27 | 6 | no | — |
| 534 | C23 | — | 27 | 6 | no | — |
| 535 | C23 | — | 27 | 6 | no | — |
| 536 | C23 | — | 27 | 6 | no | — |
| 537 | C23 | — | 27 | 6 | no | — |
| 538 | C23 | — | 27 | 6 | no | — |
| 539 | C23 | — | 27 | 3 | no | — |
| 540 | C23 | — | 36 | 12 | no | — |
| 541 | C23 | — | 54 | 12 | no | — |
| 542 | C23 | — | 108 | 6 | no | — |
| 543 | C23 | — | 108 | 6 | no | — |
| 544 | C23 | — | 108 | 4 | no | — |
| 545 | C23 | — | 108 | 12 | no | — |
| 546 | C23 | — | 108 | 12 | no | — |
| 547 | C23 | C2×D9⋊A4 | 1 | 3 | yes | complemented |
| 548 | Q8 | — | 3 | 2 | no | — |
| 549 | Q8 | — | 27 | 4 | no | — |
| 550 | Q8 | — | 27 | 4 | no | — |
| 551 | Q8 | C2×D9⋊A4 | 1 | 2 | yes | complemented |
| 552 | D4 | — | 3 | 6 | no | — |
| 553 | D4 | — | 3 | 6 | no | — |
| 554 | D4 | — | 3 | 12 | no | — |
| 555 | D4 | — | 27 | 12 | no | — |
| 556 | D4 | — | 27 | 12 | no | — |
| 557 | D4 | — | 27 | 24 | no | — |
| 558 | D4 | — | 27 | 24 | no | — |
| 559 | C2×C4 | — | 3 | 3 | no | — |
| 560 | C2×C4 | — | 3 | 6 | no | — |
| 561 | C2×C4 | — | 3 | 3 | no | — |
| 562 | C2×C4 | — | 3 | 2 | no | — |
| 563 | C2×C4 | — | 27 | 4 | no | — |
| 564 | C2×C4 | — | 27 | 4 | no | — |
| 565 | C2×C4 | — | 27 | 12 | no | — |
| 566 | C2×C4 | — | 27 | 12 | no | — |
| 567 | C2×C4 | — | 27 | 6 | no | — |
| 568 | C2×C4 | — | 27 | 6 | no | — |
| 569 | C2×C4 | — | 27 | 2 | no | — |
| 570 | C2×C3 | — | 6 | 3 | no | — |
| 571 | C2×C3 | — | 6 | 3 | no | — |
| 572 | C2×C3 | — | 48 | 2 | no | — |
| 573 | C2×C3 | — | 48 | 1 | no | — |
| 574 | C2×C3 | — | 144 | 4 | no | — |
| 575 | C2×C3 | D3×#997 | 1 | 2 | yes | — |
| 576 | C2×C3 | C2×D3×C22⋊A4 | 1 | 1 | yes | characteristic |
| 577 | D3 | — | 3 | 4 | no | — |
| 578 | D3 | — | 18 | 6 | no | — |
| 579 | C22 | — | 3 | 3 | no | — |
| 580 | C22 | — | 3 | 3 | no | — |
| 581 | C22 | — | 4 | 3 | no | — |
| 582 | C22 | — | 6 | 6 | no | — |
| 583 | C22 | — | 9 | 4 | no | — |
| 584 | C22 | — | 9 | 2 | no | — |
| 585 | C22 | — | 12 | 3 | no | — |
| 586 | C22 | — | 12 | 1 | no | — |
| 587 | C22 | — | 12 | 3 | no | — |
| 588 | C22 | — | 27 | 6 | no | — |
| 589 | C22 | — | 54 | 12 | no | — |
| 590 | C22 | — | 54 | 12 | no | — |
| 591 | C22 | — | 54 | 6 | no | — |
| 592 | C22 | — | 108 | 6 | no | — |
| 593 | C22 | — | 108 | 6 | no | — |
| 594 | C22 | — | 108 | 6 | no | — |
| 595 | C22 | — | 108 | 6 | no | — |
| 596 | C22 | D9⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| 597 | C4 | — | 3 | 2 | no | — |
| 598 | C4 | — | 3 | 2 | no | — |
| 599 | C4 | — | 27 | 4 | no | — |
| 600 | C3 | — | 48 | 1 | no | — |
| 601 | C3 | C2×D3×#997 | 1 | 1 | yes | characteristic |
| 602 | C2 | — | 6 | 3 | no | — |
| 603 | C2 | — | 6 | 3 | no | — |
| 604 | C2 | — | 9 | 4 | no | — |
| 605 | C2 | — | 54 | 6 | no | — |
| 606 | C2 | D9⋊#997 | 1 | 2 | yes | direct product factor |
| 607 | C2 | C2×D9⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D9⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C9×H(5,𝔽2) | C22×C3 |
| Frattini | C2×C3 | C2×D3×C22⋊A4 |
| Fitting | C2×C9×H(5,𝔽2) | C2×C3 |
| socle | C22×C3 | D3×C22⋊A4 |
| LCS | G ▷ C9×H(5,𝔽2) | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9⋊#997 | C2 | semidirect |
| 2. D9⋊#997 | C2 | direct (N × H) |
| 4. C2×D9×H(5,𝔽2) | C3 | semidirect |
| 6. C9⋊#997 | C22 | semidirect |
| 10. C2×C9×H(5,𝔽2) | C2×C3 | semidirect |
| 13. D9×H(5,𝔽2) | C2×C3 | semidirect |
| 30. C24×D9 | A4 | semidirect |
| 33. C9×H(5,𝔽2) | C22×C3 | semidirect |
| 47. C2×Q8×D9 | A4 | semidirect |
| 86. C24×C9 | C2×A4 | semidirect |
| 95. C23×D9 | C2×A4 | semidirect |
| 101. C2×Q8×C9 | C2×A4 | semidirect |
| 120. Q8×D9 | C2×A4 | semidirect |
| 200. C23×C9 | C22×A4 | semidirect |
| 219. Q8×C9 | C22×A4 | semidirect |
| 246. C2×H(5,𝔽2) | AGL(1,ℤ/9) | semidirect |
| 337. C2×D9 | #997 | semidirect |
| 356. H(5,𝔽2) | C2×AGL(1,ℤ/9) | semidirect |
| 435. C2×C9 | C2×#997 | semidirect |
| 438. D9 | C2×#997 | semidirect |
| 449. C24 | D9⋊A4 | semidirect |
| 466. C2×Q8 | D9⋊A4 | semidirect |
| 525. C9 | C22×#997 | semidirect |
| 547. C23 | C2×D9⋊A4 | semidirect |
| 551. Q8 | C2×D9⋊A4 | semidirect |
| 606. C2 | D9⋊#997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9⋊#997 | 2 |
| D9⋊#997 | 2 |
| C2×D3×#997 | 3 |
| C2×D9×H(5,𝔽2) | 3 |
| C22×D9⋊A4 | 4 |
| C2×D9⋊SL(2,𝔽3) | 4 |